A298762 Numbers n such that uphi(n) = uphi(n+2) - uphi(n+1), where uphi is the unitary totient function (A047994).

1, 2, 5, 21, 9177, 244965, 14307854, 24571869, 128199057, 140830365, 401767629, 420567854, 468190437, 525970977, 780768165, 886434645, 1597167645, 4046753949, 4473784821, 5364666165, 5515718205, 11175736334, 14408460165, 18026319710, 20106993885, 20357733129

Offset

1,2

Links

Table of n, a(n) for n=1..26.

Example

21 is in the sequence since uphi(21) = 12 = uphi(23) - uphi(22) = 22 - 10.

Mathematica

uphi[n_] := If[n>1, (Times @@ (Table[ #[[1]]^ #[[2]] - 1, {1} ] & /@ FactorInteger[n]))[[1]], 1]; Select[Range[10^7], uphi[#] == uphi[# + 2] - uphi[# + 1] &]

Prog

(PARI) uphi(n) = my(f=factor(n)); prod(i=1, #f~, f[i, 1]^f[1, 2]-1);
isok(n) = uphi(n) == uphi(n+2) - uphi(n+1); \\ Michel Marcus, Jan 26 2018

Crossrefs

Cf. A047994, A229552 (corresponding sequence with phi).

Sequence in context: A173313 A210575 A174143 * A025559 A072961 A249829

Adjacent sequences: A298759 A298760 A298761 * A298763 A298764 A298765

Keyword

nonn

Author

Amiram Eldar, Jan 26 2018

Extensions

a(7)-a(26) from Giovanni Resta, Jan 26 2018

Status

approved